Self-avoiding walk of 8388607 steps on the square lattice by Nathan Clisby

*** Sparse image - please zoom in, or view in full screen mode in a dark room! ***

This is a self-avoiding walk sampled from the uniform distribution via a new implementation of the pivot algorithm.

The self-avoiding walk (SAW) is an extremely simple model: a SAW is a walk on the lattice such that no lattice vertex is visited twice. However, it exactly captures the essential physics of the behaviour of polymers in a good solvent, e.g. the Flory exponent (nu) is exactly the same for SAW as it is for real polymers.

Please note that the colors are washed out because this image is extremely sparse. This is due to the fact that self-avoiding walks are fractal objects.